Have you ever wondered why ceramics are hard and brittle while metals tend to be ductile? Why some materials conduct heat or electricity while others are insulators? Why adding just a small amount of carbon to iron results in an alloy that is so much stronger than the base metal? In this course, you will learn how a material’s properties are determined by the microstructure of the material, which is in turn determined by composition and the processing that the material has undergone. This is the second of three Coursera courses that mirror the Introduction to Materials Science class that is taken by most engineering undergrads at Georgia Tech. The aim of the course is to help students better understand the engineering materials that are used in the world around them. This first section covers the fundamentals of materials science including atomic structure and bonding, crystal structure, atomic and microscopic defects, and noncrystalline materials such as glasses, rubbers, and polymers.
1.12 Eutectic Phase Diagram
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Из курса от партнера Georgia Institute of Technology
Material Processing
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Phase Diagrams and Phase Equilibria
This course picks up with an overview of basic thermodynamics and kinetics as they pertain to the processing of crystalline materials. The first module deals with phase diagrams - charts that tell us how a material will behave given a certain set of variables such as temperature, pressure, and composition. You will learn how to interpret common and complex phase diagrams and how to extract useful information from them.
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Thomas H. Sanders, Jr.Regents' Professor
School of Materials Science and Engineering
Welcome back.
In this lesson we're going to introduce a new type of phase diagram
that we are referring to as a Eutecitc Diagram.
Eutectic diagram has the morphology of the diagram that's illustrated on the board.
What we mean by the word eutectic, it actually comes from the Greek, and
it means low melting point material.
And as you look at the red arrows that are coming in,
what you're seeing is, the temperature of the liquidus
boundary is beginning to reduce as the composition of the alloy changes.
And, ultimately, it moves all the way down to a point on that
horizontal line called the eutectic point.
And so what we're going to do is to go through here,
label all of the phase fields, and
introduce some important concepts with respect to the Eutectic Phase Diagram.
So if we look at all the phase fields we have on the left side alpha,
we have on the right side beta, and we have a single phase liquid phase and
then we have, below, a two phase region of alpha plus beta.
Now, if we look at the invariant reaction,
we see that the invariant reaction is referred to as the eutectic isotherm.
If you recall, what we mean by the term invariant reaction,
it means that the number of degrees of freedom we have is equal to 0.
Now if we go back and we think about a pure substance like aluminum, for
example, aluminum melts at 660 degrees C.
And at that temperature, at constant pressure,
two phases are in equilibrium with one another, a solid phase and a liquid phase.
According to the phase rule,
what we have at that fixed pressure are two phases that are in equilibrium.
When we refer to the reaction as being invariant,
what it means is that we know that there will be two phases,
a liquid phase and a solid phase, that are in equilibrium.
But we cannot tell you how much liquid or
how much solid there is at any point in time.
And it obviously varies and goes back and fourth between liquid and solid.
Exactly the same thing happens along the Eutectic isotherm.
In other words we have three phases in equilibrium, thus giving us, for
a two component system with pressure fixed, it gives us 0 degrees of freedom.
So what that means then is,
we have the alpha phase, we have the liquid phase and the beta phase.
All three of those phases are in equilibrium.
But regardless of the overall composition of the alloy,
we can't tell which of the three phases we have with respect to their content.
We can only say that all three are going to be present.
Now what we want to do is go through and label all the phase boundaries.
Certainly the first set of phase boundaries that we've seen previously
are the boundaries we refer to as the liquidus.
Again, just like we have in the other phase diagrams in terms
of the isomorphous diagrams, we said basically that these liquidus boundaries
separate the single phase liquid field from the two phase liquid plus solid.
Sometimes when we're referring to these phase diagrams,
we might talk about the alpha branch of the liquidus,
meaning all of those alloys that are to the left of that eutectic point.
And sometimes we'll say the beta branch of the liquidus,
meaning we're looking at the alloys that are to the right of the Eutectic,
and those are rich in the amount of B that we have in the system.
Again, when we identify the solidus and once again,
that solidus is the boundary that separates the single phase solid and
the two phase liquid plus solid phase field.
And when we're looking at these boundaries here, again we have
the alpha branch of the solidus and we have the beta branch of the solidus.
The last boundary that we have that we want to include which is
an additional type of boundary, and it's referred to as the solvus boundary.
The solvus boundary essentially tells us how the solubility of
one of the components in the other changes as a function of temperature.
So when we're looking to the left, what we see is, as the temperature goes up,
the amount of B in the alpha phase progressively increases.
And likewise the amount of A in the beta phase progressively increases
with increasing temperature.
Now what you'll see periodically through these various
lessons that we're going to be describing, I have a full Eutectic Phase Diagram.
And on the diagram, I've labeled various points, and
we'll be able to use those points to make some calculations.
We're not going to be looking at all the different alloys, alloys 1 through 5, but
what you should do is, on your own, go through, do cooling curves so
that you can calculate what the compositions of the phases are and
how much of each of the phases.
Now what we're looking at here are three regions of two phase equilibrium.
Regardless of how complicated the diagram may appear, when we're doing our analysis,
we do exactly as we had done in the previous lessons
where we were describing the isomorphous diagrams.
So we focus on regions of two phase equilibrium.
So in that region of two phase equilibrium,
we can determine what the compositions of the phases are, and we can also
then determine the fractions of the phases that we have at a given temperature for
a given overall alloy composition.
When we go to three phase equilibrium, we have three phases in equilibrium.
We know what their compositions are,
those compositions are identified as those points on the Eutectic isotherm.
However, we cannot tell how much we have.
So when we look at a diagram like the Eutectic diagram,
we have single phase fields.
And in the single phase field, we know what the composition of the alloy is,
and therefore we know what the composition of the phase is.
When we get into a two phase region,
not only can we tell what the compositions of the two phases are, but we can also
determine how much of the two phases that we have in that two phase field.
In a three phase region, where we're looking at the straight line,
we can only tell what the compositions of the phases are.
So what I've done then is I've looked at Alloy number 3 from
the previous diagram and I have chosen that particular alloy and
I have come down through higher temperatures.
So I was in a liquid phase field and
came down to the two phase field as we dropped down in temperature.
Now when we hit the first point on the diagram,
which represents our liquidus temperature, at that point we have essentially all
liquid and the composition of the liquid is equal to the composition of the alloy.
We have effectively no solid present, but
we do know what the composition of that solid phase would be
in that really small, inperceptible amount of solid that we have present.
So, consequently, we know, using the tie line,
what the compositions of the phases that are present.
Now when we drop down into the two phase field below the liquidus temperature,
we have the fractions of the phases, the compositions of the phases and
we can solve everything at temperature T5, knowing that,
our overall alloy composition is equal to a value of 0.5.
So we continue to do that all the way through the table so
that we can determine the fractions of the phases as a function of temperature.
So those are the fractions that we're going to be looking for,
given the fact that we know what the composition of the alloy and
the composition of the phases that we are studying.
Now, for example, let's take a quick look at Alloy number 4.
Alloy number 4 happens to be the Eutectic composition.
And when we go through the eutectic composition,
what we find is above the Eutectic isotherm, we have 100% liquid.
Below the Eutectic isotherm, we have a mixture of two phases, alpha phase and
beta phase.
And what we can do is, we can actually make a calculation
of what the fraction of those phases are as a function of temperature.
So above the temperature T6, we have only one phase present.
That's 100% liquid.
When we reach the point at T6, what we begin to
see is we have liquid and two solids in equilibrium with one another, but
the amount of solid we have is imperceptibly small.
But as we drop below T6, what happens is both alpha phase and
beta phase increase and the amount of liquid we have now goes to 0.
So below T6, we have no liquid phase, we only have alpha plus n beta.
Now the thing that we also know is, as a check of our answers,
we know that at any particular temperature, the fraction of alpha and
the fraction of beta must equal 1.
In subsequent lessons, we're going to be looking at analyzing
these diagrams from the point of view of the phases that are present,
the compositions of the phases, and, in addition to that,
how the microstructure actually evolves as we go through a cooling process.
Thank you.
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